Let's calculate the straight line equation
To do this we will take two points from the graph
A = (0,3)
B= (2,0)
For them we will first calculate the slope of the curve
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]\begin{gathered} m=\frac{0-3}{2-0} \\ m=\frac{-3}{2} \end{gathered}[/tex]Now let's calculate the y-axis intersection
[tex]\begin{gathered} b=y-mx \\ b=3-m\cdot0 \\ b=3 \end{gathered}[/tex]The equation of the line in the slope-intercept form is
[tex]y=-\frac{3}{2}x+3[/tex]Solve and graph on a number line. 2(x-1) 4 or 2 (x-1)>4
The given inequality is:
2 (x - 1
What’s the correct answer answer asap for brainlist please
Answer:
A.it can't be endeavor.
This chart shows the cost per pound of different fruits.
From the given data, the cost per pound of apple, CP=$1.89≈$2.
We have to estimate the cost of n=3.2≈3 pounds(lb) of apple.
The cost of n=3 lb of apple can be calculated as,
[tex]\begin{gathered} T=CP\times n \\ =2\times3\text{ lb} \\ =6 \end{gathered}[/tex]Therefore, the cost of 3. pounds of apples is about $6.048.
Find the measures in the parallelogram4. Find AB and AC
Okay, here we have this:
Considering that in a parallelogram the opposite sides are congruent, we obtain the following:
AB=CD
AB=9 units
AC=BD
AC=4 units
Given the following table of values determine the value of X where f(x) has a local minimum. Assume that f is continuous and differentiable for all reals
We have to find the value of x for which f(x) has a minimum.
Extreme values of f(x), like minimum or maximum values, correspond to values of its derivative equal to 0.
In this case f'(x) = 0 for x = -2 and x = 0.
We can find if this extreme value is a minimum if the second derivative f''(x) is greater than 0.
In this case, f'(x) = 0 and f''(x) > 1 for x = 0.
Then, x = 0 is a local minimum.
Answer: x = 0
through: (5,-4), slope = -9/5
The slope intersept form of a line is ,
[tex]y-y_1=m(x-x_1)[/tex]Given the point (x1,y1) is (5,-4) and slope is -9/5 implies,
[tex]undefined[/tex]Jaylen used a 20% discount on a pair of jeans that cost $70 before tax. The sales tax is 6%. How much does the pair of jeans cost after tax? Show your work
If Jaylen used a 20% discount on a pair of jeans that cost $70 before tax, then the price of the jeans will be $70 - 20%.
Let's calculate the 20% of $70.
[tex]70\times20\%=14[/tex]So, the discounted price of the jeans before tax is $70 - $14 = $56.
Generally, sales tax is applied to the discounted price, so let's calculate the 6% of $56.
[tex]6\%\times56=3.36[/tex]The sales tax is $3.36.
Therefore, the cost of the pair of jeans after tax is $59.36.
[tex]56+3.36=59.36[/tex]HELP PLEASEEEEEEEE!!!
The rational number is -91/100 or -0.91.
What is Rational number?Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter q stands for the set of rational numbers.
The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.
Given:
We have to find the rational number between -0.45 and -0.46
Now, make both decimal into fraction
-0.45 and -0.46
-45/100 and -46/100
Now, multiply 2
-45/100 x 2/2 and -46/100 x 2/2
-90/100 and - 92/100
Hence, the rational number is -91/100 or -0.91.
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The rational number is -91/100 or -0.91.
What is Rational number?Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter q stands for the set of rational numbers.
The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.
Given:
We have to find the rational number between -0.45 and -0.46
Now, make both decimal into fraction
-0.45 and -0.46
-45/100 and -46/100
Now, multiply 2
-45/100 x 2/2 and -46/100 x 2/2
-90/100 and - 92/100
Hence, the rational number is -91/100 or -0.91.
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solve the inequality for h. h-8> 4h+5. write the answer in simplest form
Subtract '4h' from both RHS (Right-Hand side) and LHS of the inequality (Left-Hand side).
[tex]\begin{gathered} h-8-4h>4h+5-4h \\ (h-4h)-8>5+(4h-4h) \\ -3h>5 \end{gathered}[/tex]Add '8' on both LHS and RHS of the above expression.
[tex]undefined[/tex]Divide both RHS and LHS of the above expression with '-3'. Whenever an inequality is divide or multiple with a negative value, the sign of the inequality shifts. Here, the above expression is dividing with '-3'. Thus, the > symbol shifts to < symbol.
[tex]\begin{gathered} \frac{-3h}{-3}<\frac{5}{-3} \\ h<\frac{-5}{3} \end{gathered}[/tex]Thus, the iniequality for h is h<-(5/3).
Simplify the following: (4x + 3) -2(4x - 7) - 3(x +7)
Simplify: (4x + 3) -2(4x - 7) - 3(x +7)
Explanation:
[tex]\begin{gathered} (4x+3)-2(4x-7)-3(x+7) \\ =4x+3-8x+14-3x-21 \\ =4x-11x+17-21 \\ =-7x-4 \end{gathered}[/tex]Final answer: -7x-4 is required simplify form .
George filled up his car with gas before embarking on a road trip across the country. The capacity of George's gas tank is 12 gallons and her car uses 2 gallons of gas for every hour driven. Make a table of values and then write an equation for G, in terms of t, representing the number of gallons of gas remaining in George's gas tank after t hours of driving.
Given that the capacity of George's gas tank is 12 gallons and her car uses 2 gallons of gas for every hour driven.
[tex]\begin{gathered} G_{\circ}=12 \\ m=-2 \end{gathered}[/tex]slope m is negative since the gas is reducing every hour.
Writing the equation for G, in terms of t, representing the number of gallons of gas remaining in George's gas tank after t hours of driving.
[tex]\begin{gathered} G=G_{\circ}+mt \\ G=12+(-2)t \\ G=12-2t \end{gathered}[/tex]The equation for G is;
[tex]G=12-2t[/tex]Calculating the number of gallons remaining in the tank after 0,1,2 and 3 hours, we have;
[tex]\begin{gathered} G=12-2t \\ at\text{ t=0}; \\ G_0=12-2(0)=12 \\ at\text{ t=1}; \\ G_1=12-2(1)=10 \\ at\text{ t=2}; \\ G_{2_{}}=12-2(2)=12-4=8 \\ at\text{ t=3;} \\ G_3=12-2(3)=12-6=6 \end{gathered}[/tex]Completing the table, we have;
Identify the property of real numbers illustrated in the following equation.(-5) + (y · 7) = (y · 7) + (-5)
By definition, the commutative property of addition says that changing the order of addends does not change the sum, which is precisely what the equation is trying to show by changing the order of the sum, therefore, the property illustrated is the commutative property of addition.
Nikki and four friends had lunch at their favorite restaurant. The total bill was $29.00, and they wanted to leave a 15% tip. Which amount of money is closest to the 15% tip? A $3.00 B $3.50C $4.00D $4.50
Total bill = $29
Tip left = 15%
The valu of the tip = 15% of $29
[tex]\begin{gathered} \frac{15}{100}\text{ x 29} \\ \\ =\text{ \$4.35} \end{gathered}[/tex]The value of the tip = $4.35
Let us consider the options given
$4.35 - $3 = $1.35
$4.35 - $3.5 = $0.85
$4.35 - $4 = $0.35
$4.5 - $4.35 = $0.15
Looking t the deviation from the real value of the tip ($4.35), the least deviation is $0.15. Hence, we can conclude that $4.5 is the closest to the tip.
The answer is option D ($4.50)
Use the distance formula to calculate the length of the leg CD
To calculate the distance between two points on the coordinate system you have to use the following formula:
[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]Where
d represents the distance between both points.
(x₁,y₁) are the coordinates of one of the points.
(x₂,y₂) are the coordinates of the second point.
To determine the length of CD, the first step is to determine the coordinates of both endpoints from the graph
C(2,-1)
D(-1,-2)
Replace the coordinates on the formula using C(2,-1) as (x₁,y₁) and D(-1,-2) as (x₂,y₂)
[tex]\begin{gathered} d_{CD}=\sqrt[]{(2-(-1))^2+((-1)-(-2))}^2 \\ d_{CD}=\sqrt[]{(2+1)^2+(-1+2)^2} \\ d_{CD}=\sqrt[]{3^2+1^2} \\ d_{CD}=\sqrt[]{9+1} \\ d_{CD}=\sqrt[]{10} \end{gathered}[/tex]The length of CD is √10 units ≈ 3.16 units
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
Inga should use the first option that is [tex]2(x^2+6x+9)=3+18[/tex] to solve the quadratic equation.
Given equation:-
[tex]2x^2+12x-3=0[/tex]
We have to find which one of the given options are needed to solve the quadratic equation.
The given quadratic equation can be rewritten as:-
[tex]2x^2+12x[/tex]-3+3=0+3
[tex]\\2x^2+12x[/tex]-3 + 3 + 18=0 +3 +18
[tex]2x^2[/tex] + 12x + 18 = 0 + 3 + 18
Hence, the answer is the first option.
Quadratic equation
Quadratic equations are the polynomial equations of degree 2 in one variable of type [tex]f(x) = ax^2 + bx + c = 0[/tex]where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of f (x). The values of x satisfying the quadratic equation are the roots of the quadratic equation (α, β).
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Given Z VYX is bisected by YW, mZ VYX =(6r-18), and m2 VYW = 36. What is the value of r? A. 15 B. 30 C. 36 D. 72
A) 15
1) Let's sketch that
According to the Bisector Theorem, the bisected line equally divides the angle. So we can write:
∠VYW≅∠WYX
And:
6r-18 = 36+36
6r -18 = 72
6r= 90
r= 15
A data set includes weights of garbage discarded in one week from 62 different households. The paired weights of paper and glass were used to obtain the results shown to the right. Is there sufficient evidence to support the claim that there is a linear correlation between weights of discarded paper and glass? Use a significance level of α=0.05. correlation matrix: Variables Paper Glass Paper 1 0.1983 Glass 0.1983
There is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.
Given,
A data set includes weights of garbage discarded in one week from 62 different households.
significance level of α=0.05.
Now, According to the question:
The correlation matrix provided is:
Variables Paper Glass
Paper 1 0.1853
Glass 0.1853 1
The hypothesis for the test is:
H₀: ρ = 0 vs. H₀: ρ ≠ 0
The test statistic is:
r = 0.1983 ≈ 0.198
As the alternate hypothesis does not specifies the direction of the test, the test is two tailed.
The critical value for the two-tailed test is:
[tex]r_{alpha}/2, (n -2) = r_{0.005}/2 ,(62-2) = 0.250[/tex]
The conclusion is:
Because the absolute value of the test statistic is less than the positive critical value, there is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.
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lana 15:02If two events A and B are independent and you know that P(A) = 0.3, what is the value of P(A|B)?
Since the events are independent, we have the following property:
[tex]P(A)=P(A|B)[/tex]That is, the probability of A is the same as the probability of A given B (since the events are independent, event B does not affect event A).
So, if P(A) = 0.3, therefore P(A|B) is also equal to 0.3.
i need help with this too
a The value of (2.3 × 10⁴) × (1.5 × 10^-2) is 3.45 × 10^2
b. The value of (3.6 × 10^-5) ÷ (1.8 × 10^2) is 2 × 10^-3. This illustrates the concept of standard form.
What is standard form?The standard form is simply used in Mathematics to illustrate the numbers that are either too large or too small.
It's important to note that the multiplication of exponents is an addition and the division of the power is subtraction.
Therefore, (2.3 × 10⁴) × (1.5 × 10^-2) will be:
= (2.3 × 1.5) × (10^(4-2)
= 3.45 × 10^2
Also, (3.6 × 10^-5) ÷ (1.8 × 10^2) will be:
= (3.6 ÷ 1.8) × 10^(-5 + 2)
= 2 × 10^-3.
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A chef is going to use a mixture of two brands of italian dressing. the first brand contains 7% vinegar and the second brand contains 12% vinegar. the chef wants to make 280 milliliters of a dressing that is 9% vinegar. how much of each brand should she use
We know that
• The first brand contains 7% vinegar.
,• The second brand contains 12% vinegar.
,• The chef wants 280 milliliters with 9% vinegar.
Using the given information, we can express the following equation.
[tex]0.07x+0.12(280-x)=0.09(280)[/tex]Notice that 0.07x represents the first brand, 0.12(280-x) represents the second brand, and 0.08(280) represents the final product the chef wants to make.
Let's solve for x.
[tex]\begin{gathered} 0.07x+33.6-0.12x=25.2 \\ -0.05x=25.2-33.6 \\ -0.05x=-8.4 \\ x=\frac{-8.4}{-0.05} \\ x=168 \end{gathered}[/tex]Therefore, the chef needs 168 of the first brand and 112 of the second brand.Notice that 280-168 = 112.
A spherical iron ball is coated with a layer of ice of uniform thickness. If the ice melts at the rate of 8 mL/min, how fast is the outer surface area of ice changing when the outer diameter of the ball with ice on it is 24 cm?
When the outer diameter of the ball with ice on it is 24 cm then the outer surface area of ice changes at the rate of 1/90cm²/sec.
As given in the question,
Spherical ball is coated with uniform thickness.
Ice melts at the rate of 8ml/min
= (8/60)cm³/sec
Consider r as the radius of given spherical ball
Diameter = 24cm
⇒Radius 'r' =12cm
Volume 'V' = (4/3)πr³
⇒ dV /dt = (4/3)π(3r²r')
⇒-(8/60) = (4/3)π(3 ×12²×r')
⇒r' =-(8/60)×(1/576π)
⇒r' = - 1/ 4320π
Rate at which change in surface area
A =4πr²
⇒A' = 4πrr'
⇒A' = 4π (12) ( - 1/ 4320π)
= -1/90 cm²/sec.
Decrease in surface area = 1/90 cm²/sec.
Therefore, when the outer diameter of the ball with ice on it is 24 cm then the outer surface area of ice changes at the rate of 1/90cm²/sec.
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i do not understand what i am getting wrong for the 3rd question
ANSWER:
-4.1201
SOLUTION
[tex]\log _b\frac{1}{4}=\log _b1-\log _b4[/tex]this is also equivalent to
[tex]\log _b\frac{1\times7}{4\times7}=\log _b\frac{7}{28}=\log _b7-\log _b28=5.7833-9.9034=-4.1201[/tex]A bag contains 8 red marbles, 7 blue marbles and 6 green marbles. If three marbles are drawn out of the bag without replacement, what is the probability, to the nearest 10th of a percent, that all three marbles drawn will be red?
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the formula for probability
[tex]Probability=\frac{number\text{ of required outcomes}}{number\text{ of total possible outcomes}}[/tex]STEP 2: Write the outcomes of the events
[tex]\begin{gathered} number\text{ of red marbles}\Rightarrow n(red)\Rightarrow8 \\ number\text{ of blue marbles}\Rightarrow n(blue)\Rightarrow7 \\ number\text{ of green marbles}\Rightarrow n(green)\Rightarrow6 \\ number\text{ of total marbles}\Rightarrow n(total)\Rightarrow21 \end{gathered}[/tex]STEP 3: Write the formula for getting the probability that all three marbles drawn will be red
[tex]Pr(Red\text{ and Red and Red\rparen}\Rightarrow Pr(red)\times Pr(red)\times Pr(red)[/tex]STEP 4: Calculate the probability
[tex]\begin{gathered} Pr(all\text{ three are reds\rparen}\Rightarrow\frac{8}{21}\times\frac{7}{20}\times\frac{6}{19} \\ =\frac{336}{7980}=0.042105263 \\ To\text{ percentage will be to multiply by 100} \\ 4.210526316\% \\ To\text{ the nearest tenth will be:} \\ \approx4.2\% \end{gathered}[/tex]Hence, the probability, to the nearest 10th of a percent, that all three marbles drawn will be red is 4.2%
Mari pushed a cube- shaped box to explore force. She examined the attributes of the box. Does a face of her box have a right angle? Explain
The face of a cuboid box have 4 right angles.
What is mean by Cuboid?
A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.
Given that;
Mari pushed a cube- shaped box to explore force.
And, She examined the attributes of the box.
Now,
In the cube shape, faces are all squares.
And, A square is a quadrilateral in which all angles are 90 degree.
Thus, The face of a cuboid box have 4 right angles.
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(Algebra 1 Equivalent equations)
In a family, the middle child is 5 years older than the youngest child.
Tyler thinks the relationship between the ages of the ages of the children can be described with 2m-2y=10, where m is the age of the middle child and y is the age of the youngest.
Explain why Tyler is right.
Let the middle child is m and youngest is y.
The middle child is 5 years older than the youngest child, it can be shown as:
m - y = 5Tyler's equation is equivalent to ours since it can be obtained by multiplying both sides of our equation by 2:
2(m - y) = 2*52m - 2y = 10 ⇔ m - y = 5So Tyler is right.
Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. Given: XN NZ and NY = NW No; you cannot determine that the quadrilateral is a parallelogram. Yes; opposite sides are congruent. Yes; two opposite sides are both parallel and congruent. Yes; diagonals of a parallelogram bisect each other.
A parallelogram is a quadrilateral that has the following characteristics:
The opposite sides are parallel and congruent.
The opposite angles are congruent.
The consecutive angles are supplementary.
If any one of the angles is a right angle, then all the other angles will be at right angle.
The two diagonals bisect each other.
Since:
[tex]XN\cong NZ;NY\cong NW[/tex]We can conclude that the answer is:
Yes; diagonals of a parallelogram bisect each other.
The length of a rectangle is 6 cm more than the width. If the perimeter is 52 cm. What are the dimensions of the rectangle?
LA rectangle has two pairs of sides of the same length. If we call W to the width of the rectangle, we know that the length is 6cm more. If we call L the length of the rectangle:
[tex]L=W+6[/tex]The perimeter of a rectangle is twice the length plus twice the width:
[tex]Perimeter=2L+2W[/tex]Since we know that the perimeter is 52 cm, we can write the system of equations:
[tex]\begin{cases}L={W+6} \\ 2L+2W=52{}\end{cases}[/tex]We can substitute the first equation into the second one:
[tex]2(W+6)+2W=52[/tex]And solve:
[tex]2W+12+2W=52[/tex][tex]\begin{gathered} 4W=52-12 \\ . \\ W=\frac{40}{4}=10\text{ }cm \end{gathered}[/tex]We know that W = 10cm, we can now find L:
[tex]L=10+6=16\text{ }cm[/tex]Thus, the dimensions of the rectangle are:
Length: 16 cm
Width: 10 cm
Round to the nearest thousand.52.60552,605 rounded to the nearest thousand is
Find the degree measure of the central angle for sector C. (image attached)
We will determine the angle as follows:
We know that the whole circle contains 360°, so we determine the angle of 0.35 as follows:
[tex]C=\frac{0.35\ast360}{1}\Rightarrow C=126[/tex]So, the measure of the central angle for sector C is 126°.
what is the solution set for the inequality
A. x ≤ -5
B. x ≤ 5
C. x ≤ 1
d. x ≤ -14
The solution set to the inequality, 4x + 12 ≤ -8, is determined as: A. x ≤ -5.
How to Find the Solution Set of an Inequality?The solution set is the value of x that would make an inequality statement true. To find the value of x, solve as you would solve a normal equation.
Using the key to the given model in the diagram, we can write the inequality as follows:
On the left, we would have, 4x + 12.
On the right, we would have, -8.
The inequality would be expressed as:
4x + 12 ≤ -8
Solve for x
4x + 12 - 12 ≤ -8 - 12 [subtraction property of equality]
4x ≤ -20
4x/4 ≤ -20/4
x ≤ -5
The solution set is: A. x ≤ -5.
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